Spectral Norm

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Period ending 2026-09-21

2 new papers

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Period ending 2026-09-14

4 new papers

A weekly snapshot of new work published in Spectral Norm.

78 papers

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Tail-Weight Control and Localized Generalization in Nearly Low-Rank Adversarial Classification
Sep 20, 2026Kunyu Wang, Dehan Wang, Wenjun ChenSpectral Norm Empirical Risk Minimization
Stable Movement for Nondual Lipschitz Convex Optimization: Efficiency and Nearly Optimal Oracle Rates
Sep 17, 2026David Martínez-Rubio, Cristóbal GuzmánConvex Optimization Lipschitz Constant
The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings
Sep 17, 2026David Martínez-Rubio, Brian Bullins, Cristóbal Guzmán +1Convex Optimization Lipschitz Constant
On the Regularization Landscape for the Linear Recommendation Models
Sep 12, 2026Dong Li, Zhenming Liu, Ruoming Jin +4Large-Scale Recommendation Systems Spectral Norm
Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements
Sep 9, 2026Ashwin Nayak, Xingyu ZhouN$-Qubit Stabilizer States Optimal Sample Complexity
Oracle Complexity of Stochastic Fixed-Point Equations with Nonexpansive Maps
Sep 8, 2026Jelena Diakonikolas, Cristóbal Guzmán, David Martínez-RubioSharp Joint-Kl Oracle Theory Fixed-Point Iteration
Exact Recovery Thresholds for Weighted Data Selection in Vector-Valued Linear Regression
Aug 31, 2026Guangjian ZhangSpectral Norm Sparsity
Toward a First-Principles Update Geometry for the Language-Model Head
Aug 23, 2026Aditya Somasundaram, Charles Guille-Escuret, Alexander Moreno +2Spectral Norm Multi-Head Self-Attention
Exploring Oversmoothing with Householder Matrices
Aug 12, 2026Bhaskar KarolGraph Neural Networks Spectral Norm
Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples
Aug 7, 2026Xinliang Liu, Tong Mao, Jinchao XuNeural-Network Approximation Bayesian Quadrature
Tight Sample Complexity for Low-Rank Adaptation: Matching Bounds and Rank Selection
Jul 30, 2026Arunan JLow-Rank Adaptation Empirical Risk Minimization
Sharpness-Aware Minimization and Muon: Robustness under the Spectral Norm
Jul 28, 2026Wenzhi Zhong, Edward Milsom, Michael MurraySharpness-Aware Minimization Muon Optimizer
Beyond a Global Norm: Personalizing Toxicity Sensitivity in Language Models Without Retraining
Jul 25, 2026Rares A. C. Diaconescu, Iulia Slanina, Alina Florea +5Toxicity Large Language Model Alignment
Concentration and Mean-Square Bounds for Contractive Stochastic Approximation: A Unified Elementary Approach
Jul 20, 2026Siddharth ChandakStochastic Approximation Concentration Inequalities
Muse: Representation Geometry of Muon Beyond Normalized Momentum
Jul 16, 2026Da Chang, Qiankun Shi, Lvgang Zhang +4Muon Optimizer Muon
Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs
Jul 15, 2026Manuel Fernandez, Yizhe ZhuExponential Random Graph Models Latent Cluster Geometry
Cross-Trajectory Chimera Interventions Reveal Dissociable Roles of Weight Magnitude and Direction in Grokking
Jul 7, 2026Truong Xuan KhanhSynaptic Plasticity Trainability
NormGuard: Reward-Preserving Norm Constraints in Flow-Matching Reinforcement Learning
Jun 26, 2026Tianlin Pan, Lianyu Pang, Cheng Da +4Reward Gradients Reinforcement Fine-Tuning
On the stability of scale-space metrics
Jun 25, 2026William LeebWasserstein Distance Spectral Norm
The Decision Geometry of Covariance Estimation for the Global Minimum-Variance Portfolio under Heavy Tails
Jun 25, 2026Xavier FonsecaCovariance Estimation Portfolio Optimization
Tensorion: A Tensor-Aware Generalization of the Muon Optimizer
Jun 24, 2026Vladimir Bogachev, Vladimir Aletov, Alexander Molozhavenko +2Muon Optimizer Adam
Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors
Jun 24, 2026Alexander Hägele, Alejandro Hernández-Cano, Atli Kosson +1Neural Network Optimization Model Weights
Uniform Sampling from High-dimensional Spectral Norm Balls
Jun 23, 2026Michael R. MetelSpectral Norm Singular Value Decomposition
Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm
Jun 17, 2026Shan Fan, Feng Zhang, Jianjun Wang +2Tensor Completion Spectral Norm
Generalization Guarantees for Multi-Input Neural Operator Learning in Sobolev Spaces
Jun 16, 2026Yahong Yang, Zecheng Zhang, Wei Zhu +2Logarithmic Sobolev Inequalities Probabilistic Operator Learning
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
Jun 15, 2026Baicheng Li, Haizhao Yang, Shijun ZhangNeural-Network Approximation Logarithmic Sobolev Inequalities
Schattor: Schatten-family methods for deep learning optimization
Jun 14, 2026Bohao Ma, Junyu Zhang, Chuan HeStochastic Optimization Neural Network Optimization
When to use what Schatten- $p$ norm in deep learning?
Jun 13, 2026Thomas PethickSpectral Norm Muon
Free Heavy-Tailed Lunch for Muon: A Theoretical Justification of Empirical Success
Jun 12, 2026Florian Hübler, Thomas Pethick, Suvrit SraSpectral Norm Muon Optimizer
Geometric Domain Adaptation via Optimal Transport for Linear Regression in R^2
Jun 12, 2026Brian Britos, Mathias BourelDomain Adaptation Optimal Transport
Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization
Jun 8, 2026Taha BouhsineKernel Hilbert Spaces Fourier
The Tell-Tale Norm: $\ell_2$ Magnitude as a Signal for Reasoning Dynamics in Large Language Models
Jun 4, 2026Jinyang Zhang, Hongxin Ding, Yue Fang +4Large Language Model Reasoning Spectral Norm
Measuring Model Robustness via Fisher Information: Spectral Bounds, Theoretical Guarantees, and Practical Algorithms
Jun 3, 2026Chong Zhang, Xiang Li, Jia Wang +2Model Sensitivity Fisher Information
Shortcomings and capacities of real-constrained neural networks in complex spaces
Jun 3, 2026Andrew GracykNeural-Network Approximation Neural Network
Beyond $\ell_2$ -norm and $\ell_\infty$ -norm: A Curvature-Inspired $\ell_p$ -Norm Scheme for Deep Neural Networks
Jun 1, 2026Jianhao Xu, Zhuang YangNeural Network Optimization Stochastic Gradient Descent
Improved Distribution Estimation in $\ell_\infty$
May 28, 2026Doron Cohen, Aryeh Kontorovich, Yonatan LivshitzConcentration Inequalities Worst-Case
MuCon: Clipped Muon Updates for LLM Training
May 26, 2026Albert YiMuon Optimizer Muon
Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications
May 24, 2026Samuel B. Hopkins, Stefan TiegelSpectral Norm Approximation Algorithms
From SGD to Muon: Adaptive Optimization via Schatten-p Norms
May 19, 2026Thomas Massena, Corentin Friedrich, Mathieu SerrurierMuon Optimizer Optimizer Design
Optimal Reconstruction from Linear Queries
May 19, 2026Yuval Filmus, Shay Moran, Elizaveta NesterovaReconstruction Error Optimal Sample Complexity
Going PLACES: Participatory Localized Red Teaming for Text-to-Image Safety in the Global South
May 18, 2026Charvi Rastogi, Mukul Bhutani, Minsuk Kahng +13Multilingual Safety Red-Teaming
Scale-Invariant Neural Network Optimization: Norm Geometry and Heavy-Tailed Noise
May 18, 2026Jiayu Zhang, Tianyi LinNeural Network Optimization Stochastic Gradient Descent
GQA-μP: The maximal parameterization update for grouped query attention
May 14, 2026Kyle R. Chickering, Huijuan Wang, Mengxi Wu +7Model Weights Large Models
Gradient Clipping Beyond Vector Norms: A Spectral Approach for Matrix-Valued Parameters
May 12, 2026Alexander Yukhimchuk, Mladen Kolar, Martin Takáč +1Gradient Clipping Spectral Norm
Muon is Not That Special: Random or Inverted Spectra Work Just as Well
May 11, 2026Zakhar Shumaylov, Nathaël Da Costa, Peter Zaika +6Muon Optimizer Muon
Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds
May 10, 2026Yibang Li, Bihari Lal Pandey, Ravi Sah +4Muon Optimizer Muon
OrScale: Orthogonalised Optimization with Layer-Wise Trust-Ratio Scaling
May 8, 2026Yuxuan Lou, Yang YouMuon Optimizer Model Weights
Fortifying Time Series: DTW-Certified Robust Anomaly Detection
May 8, 2026Shijie Liu, Tansu Alpcan, Christopher Leckie +1Time-Series Anomaly Detection Time Series
Disagreement-Regularized Importance Sampling for Adversarial Label Corruption
May 8, 2026Csongor Horváth, Ida-Maria Sintorn, Prashant SinghImportance Sampling Importance
QuadNorm: Resolution-Robust Normalization for Neural Operators
May 8, 2026Bum Jun Kim, Makoto Kawano, Yusuke Iwasawa +1Batch Normalization Neural Operators
Sample Complexity of Stochastic Optimization with Integer Variables
May 8, 2026Hongyu Cheng, Yinghao Zheng, Marco Molinaro +1Stochastic Optimization Mixed-Integer Programming
When and Why SignSGD Outperforms SGD: A Theoretical Study Based on $\ell_1$ -norm Lower Bounds
May 7, 2026Hongyi Tao, Dingzhi Yu, Lijun ZhangStochastic Gradient Descent Riemannian Optimization
Optimal Confidence Band for Kernel Gradient Flow Estimator
May 7, 2026Yuqian Cheng, Zhuo Chen, Qian LinConfidence Intervals Wasserstein Gradient Flows
Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature
May 7, 2026Satoshi HayakawaKernel Hilbert Spaces Convex Sets
Almost-Orthogonality in Lp Spaces: A Case Study with Grok
May 6, 2026Ziang Chen, Jaume de Dios Pont, Paata Ivanisvili +2Inequalities Spectral Norm
Neural Discovery of Strichartz Extremizers
May 6, 2026Nicolás Valenzuela, Ricardo Freire, Claudio MuñozInequalities Extremes
Low Rank Tensor Completion via Adaptive ADMM
May 5, 2026Niclas Führling, Getuar Rexhepi, Giuseppe Thadeu Freitas de AbreuTensor Completion Alternating Direction Method Of Multiplier
Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
May 5, 2026Diego MarcondesPartial Differential Equation Benchmarks Logarithmic Sobolev Inequalities
Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
May 4, 2026Nicole HaoLogarithmic Sobolev Inequalities Fourier Neural Operators
Geometric and Spectral Alignment for Deep Neural Network I
May 4, 2026Ziran Liu, Wei Wang, Jinhao Wang +5Spectral Norm Residual Connections

Sep 20, 2026 · cs.LGJ/K move · Enter open · S save

Tail-Weight Control and Localized Generalization in Nearly Low-Rank Adversarial Classification

Kunyu Wang, Dehan Wang, Wenjun Chen

We study norm-constrained linear classification under Eu clidean adversarial perturbations in a Gaussian model with a low-dimen sional informative subspace and an independent noise tail. For bounded ramp loss, we prove that a principal-space witness with risk below one half forces every near-optimal predictor to have small tail weight. A path-specific density bound yields constants without requiring positive tail variance. Under isotropic principal covariance, we establish a unique population minimizer and joint local growth. Boundary normalization then removes the common attack penalty from centered margins, giving localized finite-sample guarantees governed by principal dimension and total tail energy. Globalized growth removes the entrance condition at weaker constants; a model-aware comparison retains local guarantees. Experiments with twenty paired repetitions show decreasing excess risk and tail use with sample size, and nearly unchanged behavior when tail dimension grows at fixed total energy. Pure-noise controls and optimizer diagnostics clarify the scope and limitations of these conclusions.

Spectral Norm Empirical Risk Minimization

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